rk Namespace Reference

## Variables

constexpr size_t | pmax = 3
const Float | _g2 = 1 - 1/sqrt(Float(2))
const Float | _d2 = 1 - 1/(2*_g2)
const Float | _g3 = 0.435866521508459
const Float | _b31 = -3*(_g3*_g3)/2 + 4*_g3 - 1./4
const Float | _b32 = 3*(_g3*_g3)/2 - 5*_g3 + 5./4
const Float | _a31 = -0.356
const Float | _a32 = (1/Float(3) - 2*(_g3*_g3) - 2*_b32*_a31*_g3)/(_g3*(1-_g3))
Float | alpha [][pmax+1][pmax+1]
Float | tilde_alpha [][pmax+1][pmax+1]
Float | beta [][pmax+1]
Float | tilde_beta [][pmax+1]
Float | gamma [][pmax+1]

## Variable Documentation

## pmax

constexpr size_t pmax = 3

constexpr

Examples
  burgers_diffusion_dg.cc, and runge_kutta_semiimplicit.icc.

Definition at line 27 of file runge_kutta_semiimplicit.icc.

## _g2

const Float _g2 = 1 - 1/sqrt(Float(2))

Examples
  runge_kutta_semiimplicit.icc.

Definition at line 28 of file runge_kutta_semiimplicit.icc.

## _d2

const Float _d2 = 1 - 1/(2*_g2)

Examples
  runge_kutta_semiimplicit.icc.

Definition at line 29 of file runge_kutta_semiimplicit.icc.

## _g3

const Float _g3 = 0.435866521508459

Examples
  runge_kutta_semiimplicit.icc.

Definition at line 30 of file runge_kutta_semiimplicit.icc.

## _b31

const Float _b31 = -3*(_g3*_g3)/2 + 4*_g3 - 1./4

Examples
  runge_kutta_semiimplicit.icc.

Definition at line 31 of file runge_kutta_semiimplicit.icc.

## _b32

const Float _b32 = 3*(_g3*_g3)/2 - 5*_g3 + 5./4

Examples
  runge_kutta_semiimplicit.icc.

Definition at line 32 of file runge_kutta_semiimplicit.icc.

## _a31

const Float _a31 = -0.356

Examples
  runge_kutta_semiimplicit.icc.

Definition at line 33 of file runge_kutta_semiimplicit.icc.

## _a32

const Float _a32 = (1/Float(3) - 2*(_g3*_g3) - 2*_b32*_a31*_g3)/(_g3*(1-_g3))

Examples
  runge_kutta_semiimplicit.icc.

Definition at line 34 of file runge_kutta_semiimplicit.icc.

## alpha

Float alpha[][pmax+1][pmax+1]

Initial value:
= { {},
{ {0},
{0, 1} },
{ {0},
{0, _g2},
{0, 1-_g2, _g2} },
{ {0},
{0, _g3},
{0, (1-_g3)/2, _g3},
{0, _b31, _b32, _g3} } }
rk::_b32
const Float _b32
Definition: runge_kutta_semiimplicit.icc:32
rk::_g3
const Float _g3
Definition: runge_kutta_semiimplicit.icc:30
rk::_b31
const Float _b31
Definition: runge_kutta_semiimplicit.icc:31
rk::_g2
const Float _g2
Definition: runge_kutta_semiimplicit.icc:28

Examples
  burgers_diffusion_dg.cc, and runge_kutta_semiimplicit.icc.

Definition at line 35 of file runge_kutta_semiimplicit.icc.

## tilde_alpha

Float tilde_alpha[][pmax+1][pmax+1]

Initial value:
= { {},
{ {},
{1} },
{ {},
{_g2},
{_d2, 1-_d2} },
{ {},
{_g3},
{(1+_g3)/2 - _a31, _a31},
{0, 1-_a32, _a32} } }
rk::_d2
const Float _d2
Definition: runge_kutta_semiimplicit.icc:29
rk::_a31
const Float _a31
Definition: runge_kutta_semiimplicit.icc:33
rk::_a32
const Float _a32
Definition: runge_kutta_semiimplicit.icc:34

Examples
  burgers_diffusion_dg.cc, and runge_kutta_semiimplicit.icc.

Definition at line 47 of file runge_kutta_semiimplicit.icc.

## beta

Float beta[][pmax+1]

Initial value:
= { {},
{0, 1},
{0, 1-_g2, _g2},
{0, _b31, _b32, _g3} }

Examples
  burgers_diffusion_dg.cc, burgers_diffusion_operators.icc, convect2.cc, convect_hdg.cc, dirichlet_dg.cc, dirichlet_hdg.cc, dirichlet_hdg_post.cc, dirichlet_hdg_post_rt.cc, dirichlet_hho.cc, elasticity_taylor_dg.cc, neumann_dg.cc, runge_kutta_semiimplicit.icc, and stokes_dirichlet_dg.icc.

Definition at line 59 of file runge_kutta_semiimplicit.icc.

## tilde_beta

Float tilde_beta[][pmax+1]

Initial value:
= { {},
{1},
{_d2, 1-_d2, 0},
{0, _b31, _b32, _g3} }

Examples
  burgers_diffusion_dg.cc, and runge_kutta_semiimplicit.icc.

Definition at line 64 of file runge_kutta_semiimplicit.icc.

## gamma

Float gamma[][pmax+1]

Initial value:
= { {},
{0, 1},
{0, _g2, 1},
{0, _g3, (1+_g3)/2, 1} }

Examples
  burgers_diffusion_dg.cc, helmholtz_s.cc, laplace_s.cc, level_set_sphere.cc, level_set_torus.cc, and runge_kutta_semiimplicit.icc.

Definition at line 69 of file runge_kutta_semiimplicit.icc.